Homogenization of a parabolic Dirichlet problem by a method of Dahlberg

Consider the linear parabolic operator in divergence form $$\mathcal{H} u =\partial_t u(X,t)-\text{div}(A(X)\nabla u(X,t)).$$ We employ a method of Dahlberg to show that the Dirichlet problem for $\mathcal{H}$ in the upper half plane is well-posed for boundary data in $L^p$, for any elliptic matrix of coefficients $A$ which is periodic and satisfies a Dini-type condition. This result allows us to treat a homogenization problem for the equation $\partial_t u_\varepsilon(X,t)-\text{div}(A(X/\varepsilon)\nabla u_\varepsilon(X,t))$ in Lipschitz domains with $L^p$-boundary data.Comment: 21 page

What we can learn from a comparison of the schooling systems of South Africa and Argentina

An existing accounting framework to describe an education system is elaborated and used as a framework for understanding and comparing the resource allocation policies of the South African and Argentinean schooling systems. The comparison highlights how, by paying fewer teachers more (relative to GDP per capita), South Africa is structurally forced to deal with relatively large class sizes. Both countries have attempted to use production function studies to understand ways of improving pupil performance, and in both countries the utilisation of education human resources appears particularly important. The economic case for expanding secondary schooling is perhaps not as strong as the policies, especially those in Argentina, suggest. Whilst rates of return to secondary schooling do not appear to offer concrete policy direction, a cross-country analysis that takes into account a secondary school completion ratio (a statistic calculated for this analysis) suggests that more policy emphasis should go towards improving the quality of secondary schooling.South Africa, Argentina, education policy, education financing, school, education, secondary school, educational quality

Non-vacuum initial states for the cosmological perturbations and the back-reaction problem of inflation

In the framework of Inflationary theory, the assumption that the quantum state of the perturbations is a non-vacuum state leads to a difficulty: non-vacuum initial states imply, in general, a large energy density of inflaton field quanta, not of a cosmological term type, that could prevent the inflationary phase. In this short note, we discuss in detail why this is so, keeping an eye on possible non-Gaussian features due to considering generic non-vacuum initial states.Comment: To appear in the Proceedings of the XXXVIIth Rencontres de Moriond on ``The Cosmological Model'', Les Arcs, France, March 16-23, 200

A Lagrangian effective field theory

We have continued the development of Lagrangian, cosmological perturbation theory for the low-order correlators of the matter density field. We provide a new route to understanding how the effective field theory (EFT) of large-scale structure can be formulated in the Lagrandian framework and a new resummation scheme, comparing our results to earlier work and to a series of high-resolution N-body simulations in both Fourier and configuration space. The `new' terms arising from EFT serve to tame the dependence of perturbation theory on small-scale physics and improve agreement with simulations (though with an additional free parameter). We find that all of our models fare well on scales larger than about two to three times the non-linear scale, but fail as the non-linear scale is approached. This is slightly less reach than has been seen previously. At low redshift the Lagrangian model fares as well as EFT in its Eulerian formulation, but at higher $z$ the Eulerian EFT fits the data to smaller scales than resummed, Lagrangian EFT. All the perturbative models fare better than linear theory.Comment: 19 pages, 3 figure

Nafta and industrial efficiency in Baja California

The figures before and after the North America Free Trade Agreement between Canada, Mexico and United States, suggest the intensification of the North region economic dynamics, particularly in the sates of Baja California. This paper attempts to determine whether the state’s extraordinary growth has been led by efficiency improvement or just by factor growth as a consequence of Free Trade and Foreign Direct Investment. The paper finds empirical evidence in both ways.Economic efficiency; productivity; and free trade

Effective Aligned 2HDM with a DFSZ-like invisible axion

We discuss the possibility of having a non-minimal scalar sector at the weak scale within the framework of invisible axion models. To frame our discussion we consider an extension of the Dine-Fischler-Srednicki-Zhitnitsky invisible axion model with two additional Higgs doublets blind under the Peccei-Quinn symmetry. Due to mixing effects among the scalar fields, it is possible to obtain a rich scalar sector at the weak scale in certain decoupling limits of the theory. In particular, this framework provides an ultraviolet completion of the so-called aligned two-Higgs-doublet model and solves the strong CP problem. The axion properties and the smallness of active neutrino masses are also discussed.Comment: 8 pages, 1 figure. Discussion improved, references added. Matching the journal versio